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Rub-impact between the rotating and static parts is a more common fault. The occurrence of faults is often accompanied by the generation of nonlinear phenomena. However, it is difficult to find out because the nonlinear characteristics are not obvious at the beginning of the fault. As a new frequency domain-based method, nonlinear output frequency response functions (NOFRFs) use the vibration response to extract the nonlinear characteristics of the system. This method has a better recognition rate for fault detection. Also, it has been applied in structural damages detection, but the high-order NOFRFs have the characteristics that the signals are weak and the features are difficult to extract. On this basis, the concept of the weighted contribution rate of the NOFRFs is proposed in this paper. The variable weighted coefficients with orders are used to amplify the influence of high-order NOFRFs on the nonlinearity of the system so as to extract its fault characteristics. The new index RI is proposed based on Clenshaw–Curtis quadrature formula to eliminate the effect of artificially selected weighted coefficients on sensitivity. Especially in the early stage of the fault, the new index varies greatly with the deepening of the fault. Both simulation and experimental results verify the validity and practicability of the new index. The new index has certain guiding significance in the detection of mechanical system faults.

For the nonlinear vibration problem of spur gear transmission system caused by friction and gear backlash, the dynamic model of gearbox with 16-degree-of-freedom (16-DOF) considering timevarying meshing stiffness is established by Lagrange equation. The dynamic equations of the gear system are solved by the Newmark-β method. The effects of friction coefficient, error fluctuation and meshing stiffness on the vibration response are investigated. In order to verify the validity of the model, a spur gear transmission rotor test bench was built by simulating the actual working conditions. The root mean square (RMS) is used to verify the accuracy of the model at multiple speeds, and makes up for the shortcomings of many researches without experimental argumentation. The experimental research can provide a reference for the research of gear transmission system. INDEX TERMS Spur gear transmission, precise modeling, friction coefficient, experiment validation.

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